论文标题
随机二维系统中的超延伸，具有时间反转对称性和远距离跳跃
Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping
论文作者
论文摘要
尽管人们认识到，安德森本地化都是针对所有州的$ d $或等于$ 2 $进行的，而预期的定位是在$ v（r）$减小的情况下降低或$ r^{ - d} $减小的，这是$ r^{ - d} $，dimension $ d = 2 $ d = 2 $ d = 2 $ d usping $ v（r）的本地化问题，却是$ v（r）$ r^$ res r^cos r^ress \ res r^cos r^r^r^r^ - 2^ - 2^ - - 2^ - - 2^ - 2^ - 2^ - 2^ - - 2^ - - 2^ - - 2^ - - 2^ - { - 2^ - { - 2;遵循较早的建议，我们表明，对于由二维各向异性偶极 - 偶极 - 偶极相互作用确定的，在时间反转对称性的情况下，存在两个可区分的阶段，当时弱和强障碍。第一阶段的特征是厄尔贡动力学和超级传输，而第二阶段的特征是分散尺寸的扩散运输和分离式特征态，其分形尺寸小于$ 2 $。使用定位缩放理论的扩展，并使用精确的数值对角线化对定位理论的扩展进行分析解决。
Although it is recognized that Anderson localization takes place for all states at a dimension $d$ less or equal $2$, while delocalization is expected for hopping $V(r)$ decreasing with the distance slower or as $r^{-d}$, the localization problem in the crossover regime for the dimension $d=2$ and hopping $V(r) \propto r^{-2}$ is not resolved yet. Following earlier suggestions we show that for the hopping determined by two-dimensional anisotropic dipole-dipole interactions in the presence of time-reversal symmetry there exist two distinguishable phases at weak and strong disorder. The first phase is characterized by ergodic dynamics and superdiffusive transport, while the second phase is characterized by diffusive transport and delocalized eigenstates with fractal dimension less than $2$. The transition between phases is resolved analytically using the extension of scaling theory of localization and verified numerically using an exact numerical diagonalization.
